A method for producing a non-oriented electrical steel sheet used as an iron core material for a motor or a transformer and having excellent magnetic properties comprising subjecting a raw steel material having a component composition comprising, by mass%, C: not more than 0.005%, Si: 1.0 to 5.0%, Mn: 0.04 to 3.0%, sol. Al: not more than 0.005%, P: not more than 0.2%, S: not more than 0.005%, N: not more than 0.005% and the remainder being Fe and inevitable impurities to a hot rolling to form a hot-rolled sheet, subjecting the hot-rolled sheet to a hot-band annealing and to a single cold rolling or two or more cold rollings including an intermediate annealing between each rolling to form a cold-rolled sheet having a final sheet thickness and subjecting the cold-rolled sheet to a finish annealing, in which at least one pass in the final cold rolling of the cold rolling is a rolling at a friction coefficient µ of not less than 0.030 and a rolling reduction of not less than 15%.